Chapter 22: Ratio, Proportion and Proof
Ratios
- Ratios are used to compare quantities
- You can find equivalent ratios by multiplying or dividing by the same number
- To write a ratio in its simplest form, find an equivalent ratio with the smallest possible whole number values
Problem solved
- If you use x to represent one part of the ratio, then you can write the length of the x as x
- Then form an equation and solve it to find x
Harder questions
- If the ratio contains decimals or fractions-multiply
- If the ratio has mixed units-convert to the smaller unit
Proportion
- Two quantities are in direct proportion when both quantities increase at the same rate
- Two quantities are in inverse proportion when one quantity increases at the same rate as the other quantity decreases
Divide or multiply
- You can use common sense to work out whether to divide or multiply in proportion questions
- 6 people build a wall in 4 days
- 6x4=24 so 1 person could build the wall in 24 days
- 24/8=3 so 8 people could build the wall in 3 days
Examiners report
- Show your method by writing down what you are working out at each stage of your working
- Read the question carefully-you have to write down the option which offers better value
- You won’t get the final mark if you just circle or underline your choice
Proof
- You can use algebra to prove facts about numbers
- Using algebra helps you to probe that something is true for every number
- In a proof question the working is the answer
- If the question say ‘show that’ or ‘prove that’ you need to write down every stage of your working
- If you don’t you won’t get all the marks
Golden rule
- If you need to prove something about numbers then you always use algebra
- Even number = 2n
- Odd number = 2n+1 or 2n-1
- Multiple of 3 = 3n
- Consecutive numbers = n,n+1.n+2…
- Consecutive even numbers = 2n,2n+2,2n+4…
- Consecutive odd numbers = 2n+1,2n+3,2n+5…
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